Did you know there's a scientific way to tell what colors combine to make another color? There's also a scientific way to tell what pitches combine to make another pitch. Find out more as you learn the science behind overtones and the overtone series.

Overtone: Definition

Imagine you want to touch up the paint in your living room, but don't have enough of the original paint to finish the job. Knowing that color matching with a swatch is not an exact science, you might take what little paint you have left over to the hardware store to analyze it in their paint machine. The analysis can tell you how much of what colors to add to a base paint to make that exact same color. It should be a perfect match.

The colors we see are not just one color but a combination of colors. The same thing is true about the sounds we hear in music; a musical note is not just one note but a combination of pitches called the overtone series or harmonic series. The pitch that we actually hear is called the fundamental, and all the pitches that occur over that pitch and combine to make it sound the way it does are called overtones, or harmonics.

Sound Waves

In order for us to hear a sound, there must be a sound wave produced by something that is vibrating. In music, these sound waves are produced by things such as the vibrating column of air in a flute, or the vibrating strings of a violin, or the vibrating wood of a marimba.

The length of the sound waves of the fundamental and its overtones are all related. In the chart below, you can see that the wave of the fundamental is at the bottom; this is because the fundamental is always the lowest sound of the overtone series, and it is the one we hear. Notice that the first overtone above it has waves that are half the size of the fundamental's wave. You can fit two waves of the first overtone in the space of one fundamental wave; it is half the size of the fundamental's wave.

Now look at the second overtone above the fundamental. This time you can fit three waves of this overtone in the space of the fundamental's wave. It is one-third the size of the fundamental's wave. This pattern continues all the way through the overtone series. The third overtone's wave is one-quarter the size of the fundamental's wave. The fourth overtone's wave is one-fifth the size of the fundamental's wave, and so on.

Frequencies in Hertz

Sound waves happen at a frequency that can be measured in units called Hertz (Hz). In music, we call this frequency a pitch. If you have ever been to a concert where the group tuned to a single pitch, then you have heard 440 Hz. That frequency is called an 'A,' or more precisely, 'A 440.' What you really heard at that concert was a combination of A 440 and its overtones, just like the last time you saw the color orange, you really saw a combination of red and yellow.

If you know how many Hertz are in a fundamental, it's very easy to find out how many Hertz are in each overtone: you multiply the number of Hertz by 2, then by 3, then by 4, etc. The mathematical way to say this is that the overtones are integer multiples of the fundamental, which means we multiplied the fundamental by a whole number to get them: 2, 3, 4, etc.

Let's look at an example using the pitch of 'C' that has 131 Hz. Since our fundamental has 131 Hz, then the first overtone would have twice as many, or 262 Hz. The second overtone would have three times as many, or 393 Hz and so on going up in multiples of 131 Hz.

Intervals

Musicians don't generally think in terms of frequencies and multiples when they play; they think in terms of pitches and intervals. An interval is the space between pitches and is measured in half-steps, or the distance between one key and the next on a piano keyboard.

In colors, there are stronger and weaker colors. The stronger colors of red, yellow, and blue are called the primary colors. The weaker colors of green, purple, and orange are called secondary colors. Intervals in music also range from stronger to weaker. The perfect intervals of an eighth (also called an octave), a fifth, and a fourth are strong intervals. The major and minor intervals of thirds and seconds are weaker than the perfect intervals.

These intervals are made up of the following number of half-steps, and are shown in order of strong to weak:

The Overtone Series

But how do these intervals relate to frequencies, Hertz, and pitches? We learned that the first overtone has twice as many Hertz as the fundamental. When that happens, the pitch that is produced is exactly an octave above the fundamental. So, the first overtone is an octave above the fundamental. An octave is the strongest interval, and it is the strongest overtone. The intervals in the overtone series go from strong to weak. This is what the frequencies, pitches, and intervals of the first three octaves of the overtone series look like:

Lesson Summary

A pitch that we hear, called a fundamental, is actually made up of a series of pitches that occur above it called the overtone series. These overtones can be measured in terms of frequencies called Hertz. The number of Hertz in an overtone is mathematically related to the fundamental as an integer multiple, meaning, it has twice, three times, or more the number of Hertz as the fundamental. The overtones can also be measured in distance by using intervals that tell us how many half-steps the overtones are away from each other. These intervals occur in order from strong to weak.

Lesson at a Glance

The sounds we hear in music are typically made up of a combination of pitches known as an overtone series or a harmonic series. Starting with the fundamental pitch, integer multiples are played with twice, three times, or more than the number of Hertz as the fundamental pitch.

Summary:

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